First slide

Gravitaional potential energy

Question

The ratio of the radii of the planets P₁, and P₂, is k. The ratio of the acceleration due to gravity is r. The ratio of the escape velocities from them will be

Easy

A

Kr
B

$\sqrt{kr}$
C

$\sqrt{(k / r)}$
D

$\sqrt{(r / k)}$

Solution

We know that , $v_{es} = \sqrt{(2 gR)}$
$\begin{array}{l} ∴ \frac{{(v_{es})}_{P_{1}}}{{(v_{es})}_{P_{2}}} = \frac{\sqrt{(2 g_{1} R_{1})}}{\sqrt{(2 g_{2} R_{2})}} \\ = \sqrt{(\frac{g_{1}}{g_{2}})} \times \sqrt{(\frac{R_{1}}{R_{2}})} \\ = \sqrt{kr} \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App